Elastic materials are used in clothing, particularly in undergarments. In one example, a “wing” refers to the segment of a brassiere that extends from each cup, under the shoulders, to the back strap. A brassiere has two such elastic wings, with one at each side. Traditionally, elastic wings comprise three layers of material, which includes a layer of elastic material sandwiched between a pair of stretch fabric layers. All three layers are stitched along an edge, with one of the stretch fabric layers flipped over and around the edge to conceal the stitching and to provide a hem that is five-layer thick. Brassieres and other garments made using this method are cumbersome in appearance, because such thick hems are readily visible through outer garments. Consequently, it is desirable to provide an improved elastic material that has a thinner hem and that is less cumbersome in appearance. It is also desirable to provide a method of ultrasonically cutting and bonding an elastic material.